non-Abelian Antisymmetric Tensor Fields Research Articles

Interacting Non-Abelian Anti-Symmetric Tensor Field Theories

Non-Abelian Anti-symmetric Tensor fields interacting with vector fields have a complicated constraint structure. We enlarge the gauge invariance in this system. Relevant gauge invariant quantities including the Hamiltonian are obtained. We also make introductory remarks on a different but more complicated gauge theory.

Finite BRST–antiBRST transformations in Lagrangian formalism

We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λa, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λa. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λa=saΛ, induced by a finite even-valued functional Λ(ϕ,π,λ) and by the generators sa of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕa⁎,ϕ¯ and auxiliary variables πa,λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λa, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.

A Wess-Zumino-Witten Model with Non-Abelian Antisymmetric Tensor Field(Quantum Field Theories: Fundamental Problems and Applications)

A Wess-Zumino-Witten Model with Non-Abelian Antisymmetric Tensor Field(Quantum Field Theories: Fundamental Problems and Applications)

GAUGE MODELS IN MODIFIED TRIPLECTIC QUANTIZATION

The modified triplectic quantization is applied to several well-known gauge models: the Freedman–Townsend model of non-Abelian antisymmetric tensor fields, W2 gravity, and 2D gravity with dynamical torsion. For these models we obtain explicit solutions of those generating equations that determine the quantum action and the gauge-fixing functional. Using these solutions, we construct the vacuum functional, determine the Sp(2)-invariant effective actions and obtain the corresponding transformations of extended BRST symmetry.

Supersymmetric Extension of the Non-Abelian Scalar-Tensor Duality

The field theory dual to the Freedman-Townsend model of a non-Abelian anti-symmetric tensor field is a nonlinear sigma model on the group manifold G. This can be extended to the duality between the Freedman-Townsend model coupled to Yang-Mills fields and a nonlinear sigma model on a coset space G/H. We present the supersymmetric extension of this duality and find that the target space of this nonlinear sigma model is a complex coset space, GC/HC.

Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time

Starting from a recently proposed Abelian topological model in 2+1 dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for the generalization is detected. However, we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in $D=3,$ that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore, in order to quantize the theory, we construct a complete set of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST equations using the horizontality condition.

Canonical Structure of the Non-Linear -Model in a Polynomial Formulation

We study the canonical structure of the SU(N) non-linear σ-model in a polynomial, first-order representation. The fundamental variables in this description are a non-Abelian vector field Lµ and a non-Abelian antisymmetric tensor field θµν, which constrains Lµ to be a ‘pure gauge’ (Fµν(L) = 0) field. The second-class constraints that appear as a consequence of the first-order nature of the Lagrangian are solved, and the reduced phase-space variables are explicitly found. We also treat the first-class constraints due to the gauge-invariance under transformations of the antisymmetric tensor field, constructing the corresponding most general gauge-invariant functionals, which are used to describe the dynamics of the physical degrees of freedom. We present these results in 1 + 1, 2 + 1 and 3 + 1 dimensions, mentioning some properties of the d + 1-dimensional case. We show that there is a kind of duality between this description of the non-linear σ-model and the massless Yang-Mills theory. This duality is further extended to more general first-class systems.

Supersymmetric quantum mechanics and the index theorem

We consider the classical mechanics of the spinning particle and investigate which Abelian interactions can be added without breaking supersymmetry. A quantum theory is presented. The well known index theorem for the Dirac operator is extended to take into account the effect of anti-symmetric Abelian tensor fields. Furthermore interactions with non-Abelian anti-symmetric tensor fields are investigated. It turns out in both cases that these fields do not give any non-trivial contributions to the index.

Is the Stochastic Gauge-Fixing a Consistent Method for Reducible Gauge Theories?

By using the Stochastic Gauge-Fixing term derived in a previous paper, we stochastically quantize the Non-Abelian Antisymmetric Tensor Field theory as an example of the Reducible Gauge Theories. Though all the quantities are finitely computed and the induced vertex really reproduces the full ghost contributions, the uninterpretable terms still remain.

STOCHASTIC GAUGE-FIXING FOR NON-ABELIAN ANTISYMMETRIC TENSOR FIELDS

By using the BRST invariance, we find the stochastic gauge-fixing function which corresponds to the ordinary gauge-fixing function for non-Abelian antisymmetric tensor fields as reducible gauge theories. Then the trial stochastic gauge-fixing function is obtained perturbatively.

Stochastic Quantization of Non-Abelian Antisymmetric Tensor Fields

Stochastic Quantization of Non-Abelian Antisymmetric Tensor Fields

Stochastic Quantization of Non-Abelian Antisymmetric Tensor Fields

We study the stochastic quantization of Non-Abelian Antisymmetric Tensor Fields as Reducible Gauge Theories. Then we prove that the fictitious time divergent longitudinal component reproduces the so-called Faddeev-Popov ghost effects from 1-loop contributions

GAUGE FIXING FOR LINEARIZED GRAVITY AND ANTISYMMETRIC TENSOR FIELDS

Using the functional stochastic scheme, the gauge fixing term for linearized gravity is shown to be related to longitudinal modes within the framework of the usual set of momentum projection operators. A similar analysis is done for non-Abelian antisymmetric tensor field by replacing derivatives with covariant derivatives in all relevant equations and by constructing suitable operators for projecting out transverse and longitudinal modes.

Hamiltonian BRST quantization of the interacting antisymmetric tensor field

We study the hamiltonian BRST quantization of the non-abelian antisymmetric tensor field. We find the constrained system which arises from the standard action by Dirac's procedure, and eliminate the second-class constraints by introducing Dirac brackets. Having isolated the underlying first-class constrained system, we quantize it using the hamiltonian BRST techniques of Batalin and Fradkin. We study the Lorentz covariant gauge fixing of this system, and discuss the relationship between our results and other recent studies of the interacting antisymmetric tensor field.

Quantization of non-Abelian antisymmetric tensor field

We have given a detailed derivation of a covariant expression for the S matrix of an antisymmetric tensor field on the basis of the canonical formulation of the theory. An important technical point in this derivation was the introduction of an additional gauge field with a suitable transformation law. A similar trick can be used in other theories with functionally dependent constraints, in particular, as we hope, in second-quantized models of relativistic strings. Our treatment also shows that the use of the BRST quantization method necessarily requires verification of the fulfillment of all the physical conditions, since otherwise physical unitarity of the theory may be lost.